TY - JOUR
T1 - A Linearized, Decoupled and Unconditionally Stable BDF2 Fem for the Active Fluid Model
AU - Zhang , Yuxing
AU - Wang , Bo
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 40
EP - 70
PY - 2024
DA - 2024/11
SN - 22
DO - http://doi.org/10.4208/ijnam2025-1003
UR - https://global-sci.org/intro/article_detail/ijnam/23566.html
KW - Active fluid, error estimates, auxiliary variable, BDF2, pressure-projection.
AB - <p style="text-align: justify;">In this paper, we develop a linear and decoupled fully discrete mixed finite element
scheme for the active fluid model. The scheme employs an auxiliary variable to reformulate
the fourth-order derivative term, an implicit-explicit treatment to deal with the nonlinear terms
and the second-order pressure-projection method to split the velocity and pressure. Through
rigorous theoretical analysis, the unique solvability, unconditional stability and error estimates of
the numerical scheme are obtained. Then, several numerical experiments are presented to verify
the efficiency and accuracy of the proposed scheme. Finally, the comparison of simulation results
with laboratory results, including the motion direction of active fluid changes from disorder to
order and reversal in 2D and 3D, demonstrate that the scheme can accurately capture and handle
the complex dynamics of active fluid motion.</p>